Abstract:
A statistical analysis is performed for a random unrestricted
local crew scheduling problem, expressed in terms of pairing
arrivals with departures. The analysis is aimed at
understanding the structure of similar problems with global
restrictions, and estimating their difficulty. The methods
developed are of a general nature and can be of use in other
problems with a similar structure. For large random problems,
the ground-state energy scales like N1/2
and the average excitation like N, where N is
the number of arrivals/departures. The average ground-state
degeneracy is such that the probability of hitting an optimal
pairing by chance scales like 2N2-N
for large N. By insisting on the local ground-state
energy for a restricted problem, airports can be split into
smaller parts, and the state space reduced by typically a
factor ~ 2Na, with
Na the total number of airports.